PreprintCC BY 4.0arXiv
Deriving Newton's Canonical Forms of Cubic Curves via the Center of Polynomials
Abstract
Existing classifications of real plane cubic curves rely on sophisticated tools and require a lengthy exposition. This paper provides a concise yet elementary treatment of this classical topic. Using the centers of polynomials, we establish a correspondence between the algebraic structure of these centers and geometric properties of binary cubic polynomials, which yields a novel approach to Newton's canonical forms.
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BibTeX
@misc{huang2026deriving,
title = {{Deriving Newton's Canonical Forms of Cubic Curves via the Center of Polynomials}},
author = {Hua-Lin Huang and Lili Liao and Yu Ye and Ziqi Yuan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09601},
eprint = {2609.09601},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09601},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Deriving Newton's Canonical Forms of Cubic Curves via the Center of Polynomials
AU - Hua-Lin Huang
AU - Lili Liao
AU - Yu Ye
AU - Ziqi Yuan
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09601
UR - https://arxiv.org/abs/2609.09601
AB - Existing classifications of real plane cubic curves rely on sophisticated tools and require a lengthy exposition. This paper provides a concise yet elementary treatment of this classical topic. Using the centers of polynomials, we establish a correspondence between the algebraic structure of these centers and geometric properties of binary cubic polynomials, which yields a novel approach to Newton's canonical forms.
ER -